Question: The equation of a circle $C$ is $x^2+y^2+2x+10y+25 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+2x) + (y^2+10y) = -25$ $(x^2+2x+1) + (y^2+10y+25) = -25 + 1 + 25$ $(x+1)^{2} + (y+5)^{2} = 1 = 1^2$ Thus, $(h, k) = (-1, -5)$ and $r = 1$.